I think I may have posted this in another thread, or at least I thought about it. I live at 5500 feet, and have camped at over 7000 feet and I run the stock jets. The only issue you may have is reduced output do to reduced engine power, but if all you are doing is charging your batteries, don't even worry about it.
I did it at a peak over 7000 feet on a couple ham radio Field Day weekends, and the Honda ran all weekend with no issues what so ever. It still does, but I may have changed the spark plug since then, it was a few years ago.
Those were a couple fun weekends. The land dropped off all around me, I had a 20 meter dipole up about 35 feet and pretty much worked anyone I wanted on 20 with 100 watts. Last year by a lake I almost couldn't buy a contact.